As assumed above, the electromagnetic component of the problem
is described by the vector potential. The superconductivity
is represented by the complex order parameter \(\psi \) .
The Ginzburg-Landau free energy in SI units can be written
as [1]}
\(F(\mathbf {A}, \psi ) = -\alpha |\psi |^2 + {\beta \over 2} |\psi |^4 +{1 \over 4 m } |(i \hbar \nabla + {2 e} \mathbf {A} )\psi |^2,\) 
